ML Anthology

Neural Polytopes

Koji Hashimoto, Tomoya Naito, Hisashi Naito
ICMLW 2023
/icmlw/2023/hashimoto2023icmlw-neural/

Abstract

We find that simple neural networks with ReLU activation generate polytopes as an approximation of a unit sphere in various dimensions. The species of polytopes are regulated by the network architecture, such as the number of units and layers. For a variety of activation functions, generalization of polytopes is obtained, which we call neural polytopes. They are a smooth analogue of polytopes, exhibiting geometric duality. This finding initiates research of generative discrete geometry to approximate surfaces by machine learning.

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Cite

Text

Hashimoto et al. "Neural Polytopes." ICML 2023 Workshops: SynS_and_ML, 2023.

Markdown

[Hashimoto et al. "Neural Polytopes." ICML 2023 Workshops: SynS_and_ML, 2023.](https://mlanthology.org/icmlw/2023/hashimoto2023icmlw-neural/)

BibTeX

@inproceedings{hashimoto2023icmlw-neural,
  title     = {{Neural Polytopes}},
  author    = {Hashimoto, Koji and Naito, Tomoya and Naito, Hisashi},
  booktitle = {ICML 2023 Workshops: SynS_and_ML},
  year      = {2023},
  url       = {https://mlanthology.org/icmlw/2023/hashimoto2023icmlw-neural/}
}